Analytical solution of forced convective heat transfer in tubes partially filled with metallic foam using the two-equation model

In this study, an analytical solution for fully developed forced convection in a tube partially filled with open-celled metallic foams is presented. In the foam region, the Brinkman flow model is used to describe the fluid transport, and the local thermal non-equilibrium model is adopted to represent the fluid-solid energy exchange. At the foam-fluid interface, interfacial coupling conditions for temperature are proposed and used to derive the analytical solution. Velocity and temperature profiles are derived from this solution, and explicit expressions for the friction factor and the Nusselt number are obtained. A parametric study is conducted to study the influences of various factors on flow resistance and heat transfer performance. The present analytical solution establishes a benchmark for similar work hereafter.